One of the challenges of transmitting information at high bit rates over a wireless channel is that frequency selective fading causes significant inter-symbol interference (ISI). For example, multipath in the main signal may cause delay and distortion in the signal. This is especially the case in wireless communications wherein channels are constantly changing due to signal rotation from transmitting towers and beam forming.
In the time domain, ISI is modeled by convolving the transmitted symbols with the channel impulse response. A filter, including for example, an equalizer may be used at the receive end to compensate for the distortion introduced by the channel. The goal of an equalizer is to reverse the effects of the channel, and approximate the originally transmitted symbols (i.e., realign the signal). One type of equalizer structure for providing optimal transmissions is a maximum likelihood sequence estimator (MLSE). Although the MLSE provides optimal equalization, the complexity of an MLSE grows exponentially with the length of the channel impulse response, due in part to the matrix inversion process typically implemented. A decision feedback equalizer (DFE) may be used to approximate the MLSE, but it typically provides sub-optimal approximation. An advantage of this approach is that complexity only grows linearly with the length of the channel. A DFE is a filter with two sets of filtering coefficients (taps). One set (the “forward” coefficients) are applied to the received sample stream. The second set (the “backward” or “feedback” coefficients) are applied to previous symbol decisions. The function of the backward set is to cancel the ISI due to symbols that have already been detected. The coefficient sets are jointly optimized in order to minimize a cost function. Typically, the tap values are determined using an adaptive training algorithm. The adaptive algorithm provides tap update values to the previous set of tap values, and is provided with a training sequence which it may iterative over numerous times.
Known devices for providing convergence processes for training taps of a filter measure the error in the signal and attempt to reduce that error to converge to a solution. This is typically accomplished using an iterative process that applies correction coefficients to taps within the filter. The convergence training process is terminated upon reaching a predetermined minimum error threshold. A common convergence measurement process includes setting an absolute threshold for the mean square error (MSE) value for signals equalized using the adaptive DFE. Thus, training on the taps continues until the MSE is below the pre-determined threshold. One problem with this training process is that the threshold value requires knowledge of channel conditions. If the threshold is set too high, the equalizer will stop training earlier than required, thereby degrading the system performance. On the other hand, if the threshold is too low, the equalizer performs needless training iterations. Thus, because the operating environment may constantly change, the threshold value also may need to be modified constantly. A complex process results that typically requires many iterations to converge to a solution.